Computational models for large amplitude nonlinear vibrations ofelectrostatically actuated carbon nanotube-based mass sensors

摘要

A comprehensive multiphysics model of a cantilevered carbon nanotube (CNT) including geometric andelectrostatic nonlinearities is developed. The continuous model is reduced to a finite degree of freedomsystem by the Galerkin discretization and solved using the harmonic balance method (HBM) coupled withthe asymptotic numerical method (ANM). The influence of higher modes on the nonlinear dynamics ofthe considered resonator is investigated in order to retain the number of modes which will be used bythe HBM+ANM procedure. Several simulations are performed for a specific CNT design in order to obtaina wide range of frequency shifts with respect to the mass and position of an added particle. This modelis an intuitive way for designers to develop resonant nanosensors vibrating at large amplitudes for massdetection. Particularly, it is demonstrated that the mass and position of a particle can be determinedbased on the proposed model reduced to the first bending mode coupled with the analytical expressionsof the linear frequency shifts for the second and third modes.